The lifespans of seals in a particular zoo are normally distributed. The average seal lives $13.8$ years; the standard deviation is $3.2$ years. Use the empirical rule (68-95-99.7%) to estimate the probability of a seal living between $7.4$ and $17$ years.
$13.8$ $10.6$ $17$ $7.4$ $20.2$ $4.2$ $23.4$ $95\%$ $68\%$ $13.5\%$ $13.5\%$ We know the lifespans are normally distributed with an average lifespan of $13.8$ years. We know the standard deviation is $3.2$ years, so one standard deviation below the mean is $10.6$ years and one standard deviation above the mean is $17$ years. Two standard deviations below the mean is $7.4$ years and two standard deviations above the mean is $20.2$ years. Three standard deviations below the mean is $4.2$ years and three standard deviations above the mean is $23.4$ years. We are interested in the probability of a seal living between $7.4$ and $17$ years. The empirical rule (or the 68-95-99.7 rule) tells us that $95\%$ of the seals will have lifespans within 2 standard deviations of the average lifespan. It also tells us that $68\%$ of the seals will have lifespans within 1 standard deviation of the mean. The probability of a particular seal living between $7.4$ and $17$ years is $\color{orange}{13.5\%} + {68\%}$, or $81.5\%$.